"Given the context, and the language of the [law], I would not construe it as imposing any duty on the Attorney-General to decide whether or not to refer a petition to the Court of Appeal."

Yasmin was ordered to pay the Commonwealth's costs.

Yasmin's lawyer, Sam Tierney, said his client had been disappointed by the decision.

"He remains hopeful that in light of the Human Rights Commission Report into his case and given the Commonwealth Director of Public Prosecutions has already indicated he supports a referral of Mr Yasmin's case back to the Western Australian Court of Appeal that the Attorney-General will consider his request and make a decision soon," Mr Tierney said.

Yasmin was 13 years old when he crewed a boat carrying 55 Afghan nationals to Australia in December 2009.

The Department of Immigration estimated he was about 14.

But the Australian Federal Police estimated his age at 19 after using an unreliable wrist X-ray technique.